The behavior of atoms at very low temperatures approaching absolute zero (−273.15 degrees Celsius, or 0 degrees Kelvin) results in extraordinary physical phenomena. In a system of many identical atoms at absolute zero temperature, the atoms occupy the lowest possible energy state compatible with their spin. The associated quantum statistics for elementary and composite particles relating to atoms significantly govern their behavior at very low temperatures.
All elementary particles (a particle not known to be made up of smaller particles) and composite particles are categorized into two classes, respectively referred to as “bosons” and “fermions.” Bosons and fermions are differentiated by their “spin” (the spin of a particle is its intrinsic angular momentum, and is either an integer or half-integer value, in multiples of Planck's constant); specifically, bosons have integer spin, and fermions have half-integer spin. According to the quantum mechanics “spin-statistics theorem,” which relates the spin of a particle to the statistics obeyed by that particle, only one fermion can occupy a given quantum state (the “Pauli exclusion principle”), while the number of bosons that can occupy a given quantum state is not restricted. Furthermore, bosons cause stimulated scattering of identical bosons into the same quantum state.
The basic building blocks of matter such as protons, neutrons and electrons are fermions, whereas particles such as photons and phonons, which mediate forces between matter particles, are bosons (the ability of multiple phonons to occupy a given quantum state is the principle by which a laser operates). Particles composed of a number of other particles can be either fermions or bosons, depending on their total spin. Hence, even though protons, neutrons and electrons are all fermions, it is possible for a single element (e.g., helium or He) to have some isotopes that are fermions (e.g. 3He) and other isotopes that are bosons (e.g. 4He). Sodium-23 is another example of a boson isotope. Many nuclei also are bosons; for example, the deuterium atom (an isotope of hydrogen) composed of three fermions (proton+neutron+electron) is a fermion, while its nucleus [NP] when separated from the electron is a boson. Accordingly, any nucleus with an integer spin likewise is a boson.
A Bose-Einstein condensate is a phase-coherent state of matter formed when a large number of identical bosons occupy the same quantum state. This occurs, for example, when a system of identical bosons are cooled to temperatures very near to absolute zero. Under such supercooled conditions, a large fraction of the bosons occupy the lowest quantum state (i.e., ground state). At this point, quantum effects become apparent on a macroscopic scale.
The formation of Bose-Einstein condensates is also responsible for the superfluid behavior of certain fluids. These “superfluids” are characterized by the complete absence of viscosity and quantized vorticity. Superfluidity was originally discovered in liquid helium-4 (4He); the primary difference between superfluid helium and a Bose-Einstein condensate is that the former is condensed from a liquid while the latter is condensed from a gas.
Fermionic superfluids are known as well, but because fermions are prohibited from occupying the same quantum state, fermionic superfluids generally are harder to produce. Both fermionic superfluids (e.g., 3He and cooled fermionic alkali gases such as 6Li and 40K) and “superconductors” (materials that when cooled to sufficiently low temperatures are characterized by exactly zero electrical resistance) may be described by the “BCS” theory (Bardeen, Cooper, and Schrieffer), which attributes the superconducting state and, by implication, the superfluid state of a fermionic fluid, to the formation of a Bose-Einstein condensate of “Cooper pairs.” In superconductors, Cooper pairs consist of two electrons that interact (are attracted to each other) through the exchange of phonons, and the electron pairs flow without energy dissipation. For the fermionic superfluids like 3He, the Cooper pairs consist of two fermionic helium atoms. In this manner, the behavior of the Cooper pairs may be viewed as similar to that of bosons. Under certain conditions, fermion pairs can also form diatomic molecules and undergo Bose-Einstein condensation.
In recent years, significant progress has been achieved in manipulating matter with light, and light with matter. Resonant laser fields interacting with cold, dense atom clouds provide a particularly rich system. Such light fields interact strongly with the internal electrons of the atoms, and couple directly to external atomic motion through recoil momenta imparted when photons are absorbed and emitted. Ultraslow light propagation in Bose-Einstein condensates represents an extreme example of resonant light manipulation using cold atoms. In particular, it has been shown that information relating to the phase and amplitude of an optical pulse incident on a Bose-Einstein condensate may be “stored” in the condensate in the form of an imprint on the external wavefunction components that correspond to condensate atoms in particular internal energy states. Subsequently, an optical pulse may be “revived” or regenerated from the condensate, based on the stored information relating to the incident optical pulse.